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  4. If X = 4n - 3n -1: n ∈ N and Y = 9(n -1): n ∈ N then X ∩ Y =

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Q. If $X = \{ 4^n - 3n -1 : n \in N\}$ and $Y = \{9(n -1) : n \in N \}$, then $X \cap Y = $

MHT CETMHT CET 2018

Solution:

We have,
$X=\left\{4^{n}-3 n-1: n \in N\right\} $
$=\{0,9,54, \ldots . . .\}$
$Y =\{9(n-1): n \in N\} $
$=\{0,9,18,27,36,45,54, \ldots \ldots\}$
$\therefore X \cap Y=X$